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The Prince Tower could be an option, there are rental apartments there, and the place is owned by a Korean investor.

Problem there, to be fair and honest, is that you are on the flood zone, and  besides, you do not want to get caught on foot there when darkness fall.

Another option would be to haggle a rate at the Hotel by Rua Prates by the Luz Public Gardens ( don't let the street dwellers and beggars to upset you, they are mostly

harmless ).    This place is also owned by a bunch of Korean investors.   This is a short walk towards the Rail and subway by Luz.

The new complex on Rua Anhaia, again bad location out on the woods.  Vita Bom Retiro( Rua Anhaia, 871. The building is nice, I am sure they do short term rentals, but again, you need a car to get around.  If you are on foot, even with taxicabs and Uber, the place is to far out from the core. And it is on flood zone, again.

If you can score a sublet or Air Bnb. then here are the streets you need to be on...

Rua Prates, from the Luz Rail all the way towards Rua dos Bandeirantes, you will be above flood zone.

Rua Amazonas

Avoid Rua Jose Paulino, the buildings are a bit run down, and the retail traffic is maddening.

Rua Ribeiro de Lima

Rua Lubavitch ( very quiet, but clean )

Rua Guarani

Rua Afonso Pena by the Cathedral. Cross the park, through the Police HQ building by the Praca Fernando Prestes, and you are on the Blue Line Subway Stop @ Tiradentes

Rua Tres Rios ( very charming, with some landmarks )

Rua Correia de Melo

Rua da Graça( another charming street )

Rua Silva Pinto

Rua dos Bandeirantes is a bit too quiet, and quite bluntly, most apartments there are large floor through. It's ok to get to the subway station, and above flood zone

Using the Luz Rail, stay on the Luz Public Garden Side. The opposite side, by Rua Maua, feels like you stepped into hell. You needs to be seasoned. Way too many

"Skankarellas" if you get my drift. Only good if you want to live on the wild side.

Short term rentals is out of my alley, and I am caring for my ill mother. So I have to limit my outings for a great while. 

Best of luck.

You also can score a decent location by Campos Eliseos ( do not mistake by Santa Ifigenia ).

Anything closer to Barra Funda and away from Republica by Alameda Barao de Limeira, and Alameda Eduardo Prado is safe and has good curbside appeal.

For the time being, avoid Rua Barao de Campinas, Alameda Glete, and Alameda Nothman.  There is a flat building by Avenida Rio Branco you can try. 

@Kris Kim out of curiosity, how much?

@duzzimenino i wanted to stay around 2,000 reals a month because eventually we want to take our time and look for a place to buy. but we are traveling different parts of brazil to see where we would like to settle.

@duzzimenino i wanted to stay around 2,000 reals a month because eventually we want to take our time and look for a place to buy. but we are traveling different parts of brazil to see where we would like to settle.
-@Kris Kim

At R$ 2,000, all inclusive, Bom Retiro and Campos Eliseos might be a possibility.  it's a stretch, but doable. 

You are on a 1-2BR range or sometimes a studio. 

PM if you need me to send listings.